Finite Group Databasebeta

← #14430863

Subgroups — #14430863

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756278C211yesmaximal, characteristic, complemented
2C3×#65855C211yesmaximal, characteristic
3C5×#4999C211yesmaximal, characteristic, complemented
4#11748455C211yesmaximal, characteristic, complemented
5#11748451C211yesmaximal, characteristic, complemented
6#11748367C211yesmaximal, characteristic
7C2×#90965C211yesmaximal, characteristic
8#11746889C212yesmaximal, complemented
9#11746888C212yesmaximal, complemented
10#11746888C212yesmaximal, complemented
11#11746881C212yesmaximal, complemented
12#10610821—31nomaximal, Hall
13C22×C3×D20C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15#91815C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17#91779—21no—
18#91777—21no—
19#91767—22no—
20#91759C2212yescomplemented
21#91758C2212yescomplemented
22C2×C5×#208C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4072C2211yescharacteristic
25C3×#4039—21no—
26C3×#4039—21no—
27C3×D5×C22⋊C4—22no—
28C3×C4×D20C2212yes—
29C3×C4×D20C2212yes—
30C5×C4⋊(C3⋊C8)C2212yescomplemented
31C5×C4⋊(C3⋊C8)C2212yescomplemented
32#90990C2211yescharacteristic, complemented
33#90990C2212yescomplemented
34#90990C2211yescharacteristic, complemented
35#90987C2211yescharacteristic, complemented
36#90987C2212yescomplemented
37#90987C2211yescharacteristic, complemented
38#90965C2212yes—
39#90965C2212yes—
40#90965C2212yes—
41#90965C2212yes—
42#82539—51nomaximal, Hall
43#65855D311yescharacteristic
44#65853—31no—
45C5×#424—31no—
46#65420—31no—
47#65410—31no—
48C2×#3953—31no—
49#65395—31no—
50#65136—32no—
51#65136—32no—
52#65135—32no—
53#65131—32no—
54C23×C3×D5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C2×Dic30—22no—
58C2×C3×D20—21no—
59C2×C3×D20—22no—
60C2×C3×D20Q814yescomplemented
61C2×C3×D20C2312yes—
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—22no—
64C3×C5×C4⋊C4D411yescharacteristic
65C3×C5×C4⋊C4D411yescharacteristic
66C3×C5×C22⋊C4D412yes—
67C3×C42×C5C2312yes—
68#6719—21no—
69C4⋊Dic15—22no—
70C4⋊Dic15—21no—
71C4⋊Dic15C2311yescharacteristic
72C4⋊Dic15C2312yes—
73C4⋊Dic15C2311yescharacteristic
74#6712—22no—
75#6712—22no—
76C4×Dic15—21no—
77C5×#208—22no—
78C2×C5×C3⋊C8—22no—
79C2×C5×C3⋊C8C2311yescharacteristic
80C2×C5×C3⋊C8C2311yescharacteristic
81C2×C5×C3⋊C8C2312yes—
82C3×C22⋊Dic5—21no—
83C3×#685—22no—
84C3×#685—22no—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×C4⋊Dic5C2311yescharacteristic
87C3×C4×Dic5—21no—
88C3×#518—51no—
89#5519—51no—
90#5215—51no—
91C2×#832—51no—
92#5009—52no—
93#5009—52no—
94#5008—52no—
95#5007—52no—
96#4999D511yescharacteristic, complemented
97#4998—51no—
98#4995—51no—
99C22×D20C2×D311yescharacteristic
100C2×C5×M16—31no—
101C22×C5×C8—31no—
102C5×#117C2×D311yescharacteristic
103#4072—31no—
104#4072C2×D311yescharacteristic
105C2×C4⋊Dic5—31no—
106#4039—21no—
107#4039—21no—
108#4036—61no—
109#4034—61no—
110D5×C22⋊C4—22no—
111#4024—62no—
112C4×D20C2×D312yes—
113C4×D20C2×D312yes—
114#4016—32no—
115#4015—32no—
116C5×C4⋊C8—32no—
117C5×C4⋊C8—32no—
118#3953—32no—
119#3953—32no—
120#3953—32no—
121#3953—32no—
122#3950—31no—
123#3950—32no—
124#3950—31no—
125#3949—31no—
126#3949—32no—
127#3949—31no—
128#3081—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×C3×D5—22no—
131C22×C3×D5—24no—
132C22×C3×D5—81no—
133C22×C3×D5—81no—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×Q812yes—
138C2×C3×C4×C5#4112yes—
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143C2×Dic15—81no—
144Dic30—82no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C3×D20—24no—
148C3×D20—22no—
149C3×D20C2×Q814yes—
150C3×C4×D5—82no—
151C3×C4×D5—82no—
152C5×C3⋊C8—21no—
153C5×C3⋊C8—21no—
154C5×C3⋊C8—22no—
155C22×C3×D4—51no—
156C3×C4×D4—52no—
157C3×C4×D4—52no—
158C3×C4×D4—101no—
159C3×C4×D4—101no—
160C3×#117—51no—
161C3×#117C2×D511yescharacteristic
162C2×C3×C22⋊C4—102no—
163#926—51no—
164C2×C4⋊Dic3—51no—
165C2×#208C2×D511yescharacteristic
166C22×C3⋊C8C2×D511yescharacteristic
167#890—101no—
168#888—101no—
169#878—102no—
170#870—52no—
171#869—52no—
172#832—52no—
173#832—52no—
174#832—52no—
175#832—52no—
176#808—52no—
177#808—51no—
178#808—51no—
179#807—52no—
180#807—51no—
181#807—51no—
182C4⋊(C3⋊C8)C2×D512yescomplemented
183C4⋊(C3⋊C8)C2×D512yescomplemented
184C23×D5—21no—
185C22×C4×C5C22×D311yescharacteristic
186C22×Dic5—61no—
187C2×D20—22no—
188C2×D20—21no—
189C2×D20Dic614yescomplemented
190C2×D20C22×D312yes—
191C2×C4×D5—22no—
192C2×C4×D5—22no—
193C2×Dic10—62no—
194C5×M16—62no—
195C2×C5×C8—31no—
196C2×C5×C8—31no—
197C2×C5×C8—32no—
198C2×C5×C8—62no—
199C5×C4⋊C4#6711yescharacteristic
200C5×C4⋊C4#6711yescharacteristic
201C5×C22⋊C4#6712yes—
202C42×C5C22×D312yes—
203C22⋊Dic5—21no—
204C22⋊Dic5—61no—
205#685—22no—
206#685—22no—
207C4⋊Dic5—31no—
208C4⋊Dic5—32no—
209C4⋊Dic5—31no—
210C4⋊Dic5—62no—
211C4⋊Dic5—61no—
212C4⋊Dic5C22×D311yescharacteristic
213C4⋊Dic5C22×D311yescharacteristic
214#683—62no—
215#683—62no—
216C4×Dic5—21no—
217C4×Dic5—61no—
218#544—151no—
219#518—51no—
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428—151no—
225#427—151no—
226#424—31no—
227#418—151no—
228C2×#102—151no—
229C22×C3×C5—21no—
230C22×C3×C5—21no—
231C22×C3×C5C22⋊Q812yes—
232C22×C3×C5C22×D411yescharacteristic
233C2×C3×D5—24no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—84no—
237C3×C4×C5—22no—
238C3×C4×C5—22no—
239C3×C4×C5C22⋊Q812yes—
240C3×C4×C5C22×Q811yescharacteristic
241C3×C4×C5C2×#4111yescharacteristic
242Dic15—41no—
243Dic15—42no—
244Dic15—41no—
245C3×Dic5—41no—
246C3×Dic5—41no—
247C24×C3—101no—
248C2×C3×D4—54no—
249C2×C3×D4—52no—
250C2×C3×D4—101no—
251C2×C3×D4—102no—
252C22×C3×C4—102no—
253C22×C3×C4—102no—
254C22×C3×C4C22×D511yescharacteristic
255C22×Dic3—101no—
256C2×Dic6—102no—
257C3×C4⋊C4—51no—
258C3×C4⋊C4—51no—
259C3×C4⋊C4D2011yescharacteristic
260C3×C4⋊C4D2011yescharacteristic
261C3×C22⋊C4—101no—
262C3×C22⋊C4—102no—
263C3×C22⋊C4—102no—
264C3×C22⋊C4D2012yes—
265C3×C42—101no—
266C3×C42C22×D512yes—
267#217—101no—
268C4⋊Dic3—51no—
269C4⋊Dic3—52no—
270C4⋊Dic3—51no—
271C4⋊Dic3—102no—
272C4⋊Dic3—101no—
273Dic3⋊C4—102no—
274Dic3⋊C4—102no—
275C4×Dic3—101no—
276#208—22no—
277C2×C3⋊C8—22no—
278C2×C3⋊C8C22×D511yescharacteristic
279C2×C3⋊C8C22×D512yes—
280C2×C3⋊C8C22×D511yescharacteristic
281C23×C5C2×#6711yescharacteristic
282C22×D5—22no—
283C22×D5—24no—
284C22×D5—81no—
285C22×D5—81no—
286C2×C4×C5C2×Dic612yes—
287C2×C4×C5#23512yes—
288C2×C4×C5C2×#6712yes—
289C2×C4×C5C2×#6712yes—
290C2×C4×C5C2×#6711yescharacteristic
291C2×C4×C5C23×D311yescharacteristic
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—61no—
295C2×Dic5—61no—
296C2×Dic5—62no—
297C2×Dic5—241no—
298D20—24no—
299D20—22no—
300D20C2×Dic614yes—
301C4×D5—82no—
302C4×D5—82no—
303Dic10—242no—
304C5×C8—61no—
305C5×C8—61no—
306C5×C8—62no—
307C22×D4—51no—
308C2×M16—31no—
309C22×C8—31no—
310C4⋊Q8—152no—
311C4⋊Q8—301no—
312#125—152no—
313#125—301no—
314C22⋊Q8—302no—
315C4×D4—52no—
316C4×D4—52no—
317C4×D4—101no—
318C4×D4—101no—
319#117—51no—
320#117—151no—
321#117D3×D511yescharacteristic
322C2×C4⋊C4—151no—
323C2×C22⋊C4—102no—
324#107—151no—
325#107—151no—
326#107—152no—
327#106—151no—
328#106—151no—
329#106—152no—
330C4⋊C8—32no—
331C4⋊C8—32no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102—152no—
336C2×C3×C5—22no—
337C2×C3×C5C2×C22⋊Q811yescharacteristic
338C2×C3×C5#57611yescharacteristic
339C2×C3×C5#57711yescharacteristic
340C3×D5—44no—
341C23×C3—102no—
342C23×C3—104no—
343C23×C3—401no—
344C23×C3—401no—
345C23×C3C2×D2011yescharacteristic
346C3×D4—54no—
347C3×D4—102no—
348C3×D4—104no—
349C2×C3×C4—101no—
350C2×C3×C4—101no—
351C2×C3×C4—402no—
352C2×C3×C4—402no—
353C2×C3×C4C2×D2012yes—
354C2×C3×C4C2×D2012yes—
355C2×C3×C4C2×D2011yescharacteristic
356C2×C3×C4#71112yes—
357C2×C3×C4Q8×D512yes—
358C2×C3×C4C23×D511yescharacteristic
359C2×Dic3—101no—
360C2×Dic3—101no—
361C2×Dic3—102no—
362C2×Dic3—401no—
363Dic6—402no—
364C3⋊C8—21no—
365C3⋊C8—21no—
366C3⋊C8—22no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5#92412yes—
370C22×C5C22×#6711yescharacteristic
371C2×D5—24no—
372C2×D5—42no—
373C2×D5—42no—
374C2×D5—84no—
375C4×C5—22no—
376C4×C5—22no—
377C4×C5#92412yes—
378C4×C5C22×Dic611yescharacteristic
379C4×C5C2×#23511yescharacteristic
380Dic5—41no—
381Dic5—41no—
382Dic5—121no—
383Dic5—122no—
384Dic5—121no—
385C24—101no—
386C2×Q8—302no—
387C2×D4—54no—
388C2×D4—52no—
389C2×D4—102no—
390C2×D4—101no—
391C22×C4—102no—
392C22×C4—102no—
393C22×C4—301no—
394C22×C4C2×D3×D511yescharacteristic
395M16—62no—
396C2×C8—31no—
397C2×C8—32no—
398C2×C8—31no—
399C2×C8—62no—
400C4⋊C4—51no—
401C4⋊C4—51no—
402C4⋊C4—152no—
403C4⋊C4—151no—
404C4⋊C4—151no—
405C4⋊C4—301no—
406C4⋊C4—302no—
407C4⋊C4—302no—
408C4⋊C4—302no—
409C4⋊C4#120211yescharacteristic
410C4⋊C4#120211yescharacteristic
411C22⋊C4—101no—
412C22⋊C4—102no—
413C22⋊C4—102no—
414C22⋊C4—301no—
415C22⋊C4#120212yes—
416C42—101no—
417C42—301no—
418C42C2×D3×D512yes—
419C3×C5#308111yescharacteristic, complemented, Hall
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—104no—
423C22×C3—202no—
424C22×C3—202no—
425C22×C3—404no—
426C22×C3#404312yes—
427C22×C3C22×D2011yescharacteristic
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—201no—
431C3×C4—201no—
432C3×C4#404312yes—
433C3×C4C2×#71111yescharacteristic
434C3×C4C2×Q8×D511yescharacteristic
435Dic3—201no—
436Dic3—201no—
437Dic3—202no—
438C2×C5—22no—
439C2×C5C2×#92411yescharacteristic
440C2×C5#583511yescharacteristic
441C2×C5#583611yescharacteristic
442D5—44no—
443C23—102no—
444C23—104no—
445C23—401no—
446C23—401no—
447C23C2×#120211yescharacteristic
448Q8—1202no—
449D4—54no—
450D4—102no—
451D4—104no—
452C2×C4—101no—
453C2×C4—101no—
454C2×C4—301no—
455C2×C4—301no—
456C2×C4—302no—
457C2×C4—402no—
458C2×C4—402no—
459C2×C4—1201no—
460C2×C4D5×Dic612yes—
461C2×C4#677212yes—
462C2×C4C2×#120212yes—
463C2×C4C2×#120212yes—
464C2×C4C2×#120211yescharacteristic
465C2×C4C22×D3×D511yescharacteristic
466C8—61no—
467C8—61no—
468C8—62no—
469C2×C3—22no—
470C2×C3—204no—
471C2×C3C2×#404311yescharacteristic
472C2×C3#6608511yescharacteristic
473C2×C3#6608611yescharacteristic
474C5#8253911yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—104no—
478C22—202no—
479C22—202no—
480C22—404no—
481C22#9136012yes—
482C22C22×#120211yescharacteristic
483C4—22no—
484C4—22no—
485C4—201no—
486C4—201no—
487C4—601no—
488C4—602no—
489C4—601no—
490C4#9136012yes—
491C4C2×D5×Dic611yescharacteristic
492C4C2×#677211yescharacteristic
493C3#1061082111yescharacteristic, complemented, Sylow
494C2—22no—
495C2—204no—
496C2C2×#9136011yescharacteristic
497C2#1175530911yescharacteristic
498C2#1175531111yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D20C22
hypercenter#117D3×D5
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11756278C2semidirect
3. C5×#4999C2semidirect
4. #11748455C2semidirect
5. #11748451C2semidirect
8. #11746889C2semidirect
9. #11746888C2semidirect
10. #11746888C2semidirect
11. #11746881C2semidirect
20. #91759C22semidirect
21. #91758C22semidirect
30. C5×C4⋊(C3⋊C8)C22semidirect
31. C5×C4⋊(C3⋊C8)C22semidirect
32. #90990C22semidirect
33. #90990C22semidirect
34. #90990C22semidirect
35. #90987C22semidirect
36. #90987C22semidirect
37. #90987C22semidirect
60. C2×C3×D20Q8semidirect
96. #4999D5semidirect
182. C4⋊(C3⋊C8)C2×D5semidirect
183. C4⋊(C3⋊C8)C2×D5semidirect
189. C2×D20Dic6semidirect
419. C3×C5#3081semidirect
474. C5#82539semidirect
493. C3#10610821semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117562782
C3×#658552
C5×#49992
#117484552
#117484512
#117483672
C2×#909652
#117468892
#117468882
#117468812
#106108213
#825395